The meaning of the game is fairly obvious to me (though I'm sure there are other valid interpretations). I'm going to use politics as an example, though it can apply to other things (religion, economy, basically any argument). Let's say your on the far left, Black. Everything they say sounds pretty good, it could fix the country! You spread the word around, using all their scare-tactics about the other side and high-handed goals. You manage to convince people. But things go left for a while, and everything they said didn't happen. They were wrong! It's time to try right, White.
They're trying to warn people about everything wrong with Left. They have goals that could actually work. You take up the propaganda, and convince as many people as possible. But again, things go right for awhile, and nothing they said happens. But left has improved a bit...
Back and forth, until you realize that the truth does not lie at extremes. (non-political example) If a man says men are better than women, it's almost guaranteed that a nearby female will tell him women are better than men. But neither is true, both sides have strength and weaknesses. You become gray, in-between. But when the argument breaks out and both extremes are screaming, no one listens to the peoples saying 'you're both part right and part wrong'. People like extremes, and are rarely convinced by the in-between, no matter how valid. Your words just pass right through.
The game gets it's point across beautifully.